Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 7 of 7
Full-Text Articles in Statistics and Probability
On Likelihood Ratio Tests When Nuisance Parameters Are Present Only Under The Alternative, Cz Di, K-Y Liang
On Likelihood Ratio Tests When Nuisance Parameters Are Present Only Under The Alternative, Cz Di, K-Y Liang
Chongzhi Di
In parametric models, when one or more parameters disappear under the null hypothesis, the likelihood ratio test statistic does not converge to chi-square distributions. Rather, its limiting distribution is shown to be equivalent to that of the supremum of a squared Gaussian process. However, the limiting distribution is analytically intractable for most of examples, and approximation or simulation based methods must be used to calculate the p values. In this article, we investigate conditions under which the asymptotic distributions have analytically tractable forms, based on the principal component decomposition of Gaussian processes. When these conditions are not satisfied, the principal …
Proportional Mean Residual Life Model For Right-Censored Length-Biased Data, Gary Kwun Chuen Chan, Ying Qing Chen, Chongzhi Di
Proportional Mean Residual Life Model For Right-Censored Length-Biased Data, Gary Kwun Chuen Chan, Ying Qing Chen, Chongzhi Di
Chongzhi Di
To study disease association with risk factors in epidemiologic studies, cross-sectional sampling is often more focused and less costly for recruiting study subjects who have already experienced initiating events. For time-to-event outcome, however, such a sampling strategy may be length-biased. Coupled with censoring, analysis of length-biased data can be quite challenging, due to the so-called “induced informative censoring” in which the survival time and censoring time are correlated through a common backward recurrence time. We propose to use the proportional mean residual life model of Oakes and Dasu (1990) for analysis of censored length-biased survival data. Several nonstandard data structures, …
Multilevel Latent Class Models With Dirichlet Mixing Distribution, Chong-Zhi Di, Karen Bandeen-Roche
Multilevel Latent Class Models With Dirichlet Mixing Distribution, Chong-Zhi Di, Karen Bandeen-Roche
Chongzhi Di
Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we consider multilevel latent class models, in which sub-population mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when …
Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang
Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang
Chongzhi Di
We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a special case of two component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. It has been widely used in genetic linkage analysis under heterogeneity, in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard and the LRT statistic does not converge to a conventional 2 distribution. In this paper, we investigate the asymptotic behavior of the LRT for …
Multilevel Functional Principal Component Analysis, Chong-Zhi Di, Ciprian M. Crainiceanu, Brian S. Caffo, Naresh M. Punjabi
Multilevel Functional Principal Component Analysis, Chong-Zhi Di, Ciprian M. Crainiceanu, Brian S. Caffo, Naresh M. Punjabi
Chongzhi Di
The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each subject, at two visits. The volume and importance of this data presents enormous challenges for analysis. To address these challenges, we introduce multilevel functional principal component analysis (MFPCA), a novel statistical methodology designed to extract core intra- and inter-subject geometric components of multilevel functional data. Though motivated by the SHHS, the proposed methodology is generally applicable, with potential relevance to many modern scientific …
Nonparametric Signal Extraction And Measurement Error In The Analysis Of Electroencephalographic Activity During Sleep, Ciprian M. Crainiceanu, Brian S. Caffo, Chong-Zhi Di, Naresh M. Punjabi
Nonparametric Signal Extraction And Measurement Error In The Analysis Of Electroencephalographic Activity During Sleep, Ciprian M. Crainiceanu, Brian S. Caffo, Chong-Zhi Di, Naresh M. Punjabi
Chongzhi Di
We introduce methods for signal and associated variability estimation based on hierarchical nonparametric smoothing with application to the Sleep Heart Health Study (SHHS). SHHS is the largest electroencephalographic (EEG) collection of sleep-related data, which contains, at each visit, two quasi-continuous EEG signals for each subject. The signal features extracted from EEG data are then used in second level analyses to investigate the relation between health, behavioral, or biometric outcomes and sleep. Using subject specific signals estimated with known variability in a second level regression becomes a nonstandard measurement error problem.We propose and implement methods that take into account cross-sectional and …
Generalized Multilevel Functional Regression, Ciprian M. Crainiceanu, Ana-Maria Staicu, Chong-Zhi Di
Generalized Multilevel Functional Regression, Ciprian M. Crainiceanu, Ana-Maria Staicu, Chong-Zhi Di
Chongzhi Di
We introduce Generalized Multilevel Functional Linear Models (GMFLMs), a novel statistical framework for regression models where exposure has a multilevel functional structure. We show that GMFLMs are, in fact, generalized multilevel mixed models. Thus, GMFLMs can be analyzed using the mixed effects inferential machinery and can be generalized within a well-researched statistical framework. We propose and compare two methods for inference: (1) a two-stage frequentist approach; and (2) a joint Bayesian analysis. Our methods are motivated by and applied to the Sleep Heart Health Study, the largest community cohort study of sleep. However, our methods are general and easy to …